Stiffness reconstruction methods for MR elastography

Abstract

Assessment of tissue stiffness is desirable for clinicians and researchers, as it is well established that pathophysiological mechanisms often alter the structural properties of tissue. Magnetic resonance elastography (MRE) provides an avenue for measuring tissue stiffness and has a long history of clinical application, including staging liver fibrosis and stratifying breast cancer malignancy. A vital component of MRE consists of the reconstruction algorithms used to derive stiffness from wave‐motion images by solving inverse problems. A large range of reconstruction methods have been presented in the literature, with differing computational expense, required user input, underlying physical assumptions, and techniques for numerical evaluation. These differences, in turn, have led to varying accuracy, robustness, and ease of use. While most reconstruction techniques have been validated against in silico or in vitro phantoms, performance with real data is often more challenging, stressing the robustness and assumptions of these algorithms. This article reviews many current MRE reconstruction methods and discusses the aforementioned differences. The material assumptions underlying the methods are developed and various approaches for noise reduction, regularization, and numerical discretization are discussed. Reconstruction methods are categorized by inversion type, underlying assumptions, and their use in human and animal studies. Future directions, such as alternative material assumptions, are also discussed.

Magnetic resonance elastography of skeletal muscle deep tissue injury

“…Full details of the inversion algorithm implemented in the ROOT data analysis framework (ROOT 5.34/17, CERN, Meyrin, Switzerland) were previously described by Sinkus et al To review briefly, the slice, phase, frequency and reference encoded MRE phase images were unwrapped and filtered using a three‐dimensional Gaussian filter with 3 x 3 x 3 support and σ = 1 voxel. To remove the compressional wave component the curl was calculated on a stencil of 3 x 3 x 3 pixels, followed by reconstruction of the viscoelastic maps using the direct inversion method …”

An analytical solution to the dispersion‐by‐inversion problem in magnetic resonance elastography

“… and denote central first‐ and second‐order finite difference kernels, respectively, which are typically used in MRE inversion techniques 13,15 . Central difference operators are often applied in MRE because other nonsymmetric stencils neglect information from one direction.…”

“…MRE generates parameter maps from time‐harmonic shear wavefields using inverse problem solutions 7 . Inverse methods in MRE published in the literature differ by their treatment of noise, boundary conditions, and tissue properties including heterogeneity, compressibility, anisotropy, and viscosity 8‐13 . Nonetheless, most MRE inversion methods are similar in that they yield parameter maps with a spatial resolution above the diffraction limit, thus providing super‐resolution.…”

“…7 Inverse methods in MRE published in the literature differ by their treatment of noise, boundary conditions, and tissue properties including heterogeneity, compressibility, anisotropy, and viscosity. [8][9][10][11][12][13] Nonetheless, most MRE inversion methods are similar in that they yield parameter maps with a spatial resolution above the diffraction limit, thus providing super-resolution. To achieve this, fine features of the curvature of shear waves are analyzed, often by applying finite-difference operators (FDOs) to the wave images.…”

Stabilized finite elements for time‐harmonic waves in incompressible and nearly incompressible elastic solids

“…Elastomeric materials, for example, are often accurately modeled as incompressible, and modeling their dynamical response is of current interest in understanding elastomeric actuators . Biological tissues are also often modeled as incompressible elastic or viscoelastic materials, and propagation of shear elastic waves in such media is of interest in a new medical imaging field called elastography . Therefore, it is of interest to have accurate, efficient, and stable methods to compute elastic wave fields in incompressible and nearly incompressible materials.…”